Table 1.

Average relative difference percentages (between solutions for insulating membrane vs. homogeneous space) for electric potential, longitudinal electric field, and line derivative of the longitudinal field (the activating function) distributions along axon centerlines for the 60-axon bundle in Fig. 4a. Only 40 axons, which have exactly three continuous combined centerline paths illustrated in Fig. 4b,c, were retained. Relative signed $\left|E_z\right|$ differences at the terminations were computed at the center of the hemispherical closing cap. The corresponding standard deviations are shown by superscripts.

Testing case	Combined path #1	Combined path #2	Combined path #3
Axons diam.	Hack’s level 1 – 2 μm	Hack’s level 2 – 1 μm	Hack’s level 3 – 1 μm
Rel. potential ${\varphi }_{\mathrm{e}}$ diff. (L2 norm)	0.005% 0.001%	0.003% 0.001%	0.003% 0.001%
Rel. $E_{\mathrm{z}}$ diff. (L2 norm)	0.2% 0.1%	0.5% .0.2%	0.5% 0.4%
Rel. $d{E}_{\mathrm{z}}/dz$ diff. (L2 norm)	112% 63%	106% 80%	87% 92%
Rel. $\left|E_{\mathrm{z}}\right|$ diff. at start termination	+16.1% .0.2%	+16.4% 0.5%	+16.4% 0.5%
Rel. $\left|E_{\mathrm{z}}\right|$ diff. at end termination	+16.1% 0.2%	+16.0% 0.3%	+14.9% 0.3%
The same results for the refined axonal meshes (1:4 barycentric triangle subdivision)
Rel. potential ${\varphi }_{\mathrm{e}}$ diff. (L2 norm)	0.005% 0.001%	0.003% 0.001%	0.003% 0.001%
Rel. $E_{\text{z}}$ diff. (L2 norm)	0.2% 0.1%	0.5% 0.2%	0.5% 0.4%
Rel. $d{E}_{\mathrm{z}}/dz$ diff. (L2 norm)	112% 63%	106% 81%	85% 90%
Rel. $\left|E_{\mathrm{z}}\right|$ diff. at start termination	+16.1% .0.1%	+16.4% 0.3%	+16.4% 0.8%
Rel. $\left|E_{\mathrm{z}}\right|$ diff. at end termination	+16.1% 0.3%	+16.0% 0.3%	+15.0% 0.7%